For each of the following $5$ statements, select True $($if you believe the statement is true$)$ and False $($if you believe the statement is false$).$

$($a$)$

$[$ Select $]$

If f$($n$)$ in O$($n$2)$ and g$($n$)$ in $\backslash$Theta $($n$),$ then f$($n$)+$ n $\backslash$times g$($n$)$ in $\backslash$Theta $($n$2).$

$($b$)$

$[$ Select $]$

If f$($n$)$ in O$($n$)$ and g$($n$)$ in O$($n$2),$ then n $\backslash$times f$($n$)+$ g$($n$)$ in $\backslash$Theta $($n$2).$

$($c$)$

$[$ Select $]$

If f$($n$)$ in O$($n$),$ then n $\backslash$times f$($n$)+2000$n in $\backslash$Theta $($n$2).$

$($d$)$

$[$ Select $]$

If f$($n$)$ in O$($n$),$ then n $\backslash$times f$($n$)+2000$n$2$ in $\backslash$Theta $($n$2).$

$($e$)$

$[$ Select $]$

n$!$ in O$(2$n$).$